Simplify the following expression and state the condition under which the simplification is valid. $p = \dfrac{a^2 - 4}{a - 2}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = a$ $ b = \sqrt{4} = -2$ So we can rewrite the expression as: $p = \dfrac{({a} {-2})({a} + {2})} {a - 2} $ We can divide the numerator and denominator by $(a - 2)$ on condition that $a \neq 2$ Therefore $p = a + 2; a \neq 2$